#### For citation:

Serykh I. V., Sonechkin D. M. Chaos and order in atmospheric dynamics part 1. Chaotic weather variations. *Izvestiya VUZ. Applied Nonlinear Dynamics*, 2017, vol. 25, iss. 4, pp. 4-22. DOI: 10.18500/0869-6632-2017-25-4-4-22

# Chaos and order in atmospheric dynamics part 1. Chaotic weather variations

Ideas of temporary energy distributions of large-scale atmospheric motions are made more accurately in the range of scales from days to one year in order to solve the problem of the chaos and order co-existence in the weather and climate dynamics. Spectra of the Blinova’s mean and shifted zonal extratropical flow indices as well as spectra of the tropical Southern Oscillation and El Nino indices are used for this purpose. Unlike earlier had ideas, it is found for the Blinova indices that transitions between the parts of the spectrum ranges having different average inclinations happen smoothly so there is no «synoptic maximum» of the spectral density near the period about one week and no «index cycle maximum» near the period of about two-three weeks. It confirms a chaoticity of the extratropical weather variations. As for the tropical indices, a break of the spectral density curve is found at the period of 5 days, which has been earlier noticed only in the dynamics of some local characteristics of tropical weather. The second break is found at the period of about 45 days for the modified index of the Southern Oscillation where a peak in the spectrum of the Madden–Julian Oscillation has been earlier found. These breaks indicate the existence of an «order» in the tropical weather dynamics, which also is chaotic, in general. Spectra of the monthly and seasonal weather variations everywhere on the Earth are found composed from a seemingly continuous background and some delta peaks imposed on this background. As a result, the dynamics consists of a mix of partly chaotic and partly ordered weather variations.

- Lorenz E.N. Atmospheric predictability experiments with a large numerical model. Tellus. 1982. Vol. 34. P. 505–513.
- Bengtsson L., Hodges K.I. A note on atmospheric predictability. Tellus A. 2005. Vol. 58. No. 1. P. 154–157.
- Bengtsson L., Hodges K.I., Froude L.S.R. Global observations and forecasting skill. Tellus A. 2005. Vol. 57. No. 4. P. 515–527.
- Froude L.S.R., Bengtsson L., Hodges K.I. Atmospheric predictability revisited. Tellus A. 2013. Vol. 65i0, doi:10.3402/tellusa.v65i0.19022
- Bunimovich L.A. Short- and long-term forecast for chaotic and random systems. Nonlinearity. 2014. Vol. 27. P. R51–R60.
- Cullen, M.J.P. The Unified Forecast/Climate Model. Meteorol. Magazine. 1993. Vol. 122. P. 81–94.
- Palmer T.N., Doblas-Reyes F.J., Weisheimer A., Rodwell M.J. Toward seamless prediction: calibration of climate change projections using seasonal forecasts. Bull. Amer. Meteorol. Soc., 2008. Vol. 89. No. 4. P. 459–470.
- Arnold V.I., Afraimovich V.S., Ilyashenko Yu.S., Shilnikov L.P. Teoriya bifurkatsiy. V knige: Dinamicheskiye sistemy–5, Itogi Nauki i Tekhniki. Ser. Sovrem. probl. mat. fund. napr., 5, M.: VINITI. 1986. P. 5–218 (in Russian).
- Eliasen E., Machenhauer B. On the observed large-scale atmospheric wave motions. Tellus. 1969. Vol. 21. P. 149–166.
- Wiin-Nielsen A. On the annual variation and spectral distribution of atmospheric energy. Tellus. 1967. Vol. 19. P. 540–558.
- Wiin-Nielsen A., Chen T.-C. Fundamentals of Atmospheric Energetics. New York, NY: Oxford University Press, 1993. 376 p.
- Monin A.S., Yaglom A.M. Statisticheskaya gidromekhanika. 2nd ed., St. Petersburg: Gidrometeoizdat, 1996. Vol. 2. 742 p. (in Russian).
- Mirabel A.P., Monin A.S. Two-dimensional turbulence. Uspekhi Mekhaniki. 1979. Vol. 2. No. 3. P. 47–95 (in Russian).
- Danilov S.D., Gurarie D. Quasi-two-dimensional turbulence. Phys. Usp. 2000. Vol. 43. P. 863–900.
- Lilli D.K. Numerical simulation of two-dimensional turbulence. Phys. Fluids. Suppl. II. 1969. Vol. 12. II-240 – II-249.
- Shapovalova N.S. Proceedings of the Hydrometeorological Center of the USSR. 1987. Issue. 278. Pp. 90–99 (in Russian).
- Taylor G.I. The spectrum of turbulence. Proc. R. Soc. London. Ser A. Vol. 164. P. 476–490.
- Starr V.P. Physics of Negative Viscosity Phenomena. New York: McGraw-Hill, 1968.
- Monin A.S. Hydrodynamic theory of short-range weather forecasts. Sov. Phys. Usp. 1969. Vol.11. P. 746–767.
- Vinogradskaya A.A., Vlasova I.L., Datsenko N.M., Sonechkin D.M. Proceedings of the USSR Hydrometeorological Center. 1988. Issue. 297. P. 150–165 (in Russian).
- Ogura Y. Energy transfer in a normally distributed and isotropic turbulent velocity field in two dimension. Physics Fluids. 1962. Vol. 5. No. 4. P. 395–401.
- Namias J. The index cycle and its role in the general circulation. J. Meteorol. 1950. Vol. 8. P. 131–140.
- Webster P.J., Keller J.L. Atmospheric variations: vacillation and index cycle. J. Atmos. Sci. 1975. Vol. 32. P. 1283–1300.
- Dickey J.O., Ghil M., Marcus S.L. Extratropical aspects of the 40-50 day oscillation in length-of-day and atmospheric angular momentum. J. Geophys. Res.: Atmosphere. 1991. Vol. 96. No. D12. P. 22643–22658.
- Lovejoy S., Schertzer D. Scale invariance in climatological temperatures and the spectral plateau. Annales Geophysicae. 1986. Vol. 4B. P. 401–410.
- Blinova E.N., Marchuk G.I. Proceedings of the Institute of Atmospheric Physics of the Academy of Sciences of the USSR. 1958. No. 2. P. 106–113 (in Russian).
- Marchuk G.I. Proceedings of the Institute of Atmospheric Physics of the Academy of Sciences of the USSR. 1958. No. 2. P. 114–118 (in Russian).
- Compo G.P., Whitaker J.S., Sardeshmukh P.D. et al. The Twentieth Century Reanalysis Project. Quarterly J. Roy. Meteorol. Soc. 2011. 137. P. 1–28.
- Saltzman B., Fleisher A. The exchange of kinetic energy between larger scales of atmospheric motions. Tellus. 1960. Vol. 12. P. 374–377.
- Saltzman B., Teweles S. Further statistics on the exchange of kinetic energy between harmonic components of the atmospheric flow. Tellus. 1964. Vol. 16. P. 432–435.
- Silberman I. Planetary waves in the atmosphere. J. Meteorol. 1954. V. 11. P. 27-34.
- Elsaesser H.W. Evaluation of spectral versus grid methods of hemispheric numerical weather prediction. J. Appl. Meteorol. 1966. Vol. 5. P. 246–262.
- Madden R.A., Julian P.R. Observations of the 40–50 day tropical oscillation – a review. Mon. Wea. Rev. 1994. Vol. 122. P. 814–837.
- Donald A., Meinke H., Power N., de Maia H.N., Wheeler M.C., White N., Stone R.C., Ribbe J. Near-global impact of the Madden – Julian Oscillation on rainfall. Geophys. Res. Lett. 2006. Vol. 33. L09704.
- Zhang C. Madden – Julian Oscillation. Bringing weather and climate. Bull. Amer. Meteor. Soc. 2013. Vol. 94. P. 1849–1870.
- Huybers P., Curry W. Links between annual, Milankovitch and continuum temperature variability. Nature. 2006. Vol. 441. P. 329–332.
- Saffman P.G. A note on the spectrum and decay of random two-dimensional vorticity distributions at large Reynolds number. Studies in Applied Mathematics. 1971. Vol. 50. No. 4. P. 377–383.

- 1493 reads